The irrational number e is also known as Euler’s number. It is
approximately 2.718281, and is the base of the natural logarithm,
ln (this means that, if ,
then . For real input, exp(x) is always positive.

For complex arguments, x=a+ib, we can write
. The first term, , is already
known (it is the real argument, described above). The second term,
, is , a function with magnitude
1 and a periodic phase.